Is there a more evil number than Belphegor's Prime...Don't miss the extra footage on Numberphile2: https://youtu.be/9CcI5M1LfRs
More links & stuff in full description below ↓↓↓
This video features ProfessorTonyPadilla from the University of Nottingham.
More Tony videos: http://bit.ly/Padilla_Numberphile
666 video: https://youtu.be/UkZqFtYtqaI
BeastlyPrimes: https://oeis.org/A131645
Belphegor Primes: https://oeis.org/A232448
Republican Primes: https://oeis.org/A125524
Democratic Primes: https://oeis.org/A125523
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
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Sign up for (occasional) emails: http://eepurl.com/YdjL9

published:31 Oct 2018

views:128672

FeaturingNeil Sloane from the Online Encyclopedia of Integer Sequences (OEIS). LunarArithmetic (aka Dismal Arithmetic)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of the OEIS: https://oeis.org
Lunar Primes: https://oeis.org/A087097
Lunar Squares: https://oeis.org/A087019
The original paper on lunar arithmetic (formerly dismal arithmetic) by David Applegate, Marc LeBrun, and Neil Sloane: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdfSloane's Gap: https://youtu.be/_YysNM2JoFo
Six Sequences: https://youtu.be/VDD6FDhKCYA
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Patreon: http://www.patreon.com/numberphile
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
----------------
As expected many people ask "what is the point of this"... And fair enough.
Rather than answering everyone individually, here is my view (I am just the film-maker, not a mathematician)
- Brady
↓↓↓
1. Because it is fun and creative - and playing with new ideas is good for your brain.
2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that.
Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope not!!!)... But neither is it just throwing ALL rules out of the window... It is creating a new arbitrary set of rules and seeing what happens...
What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics?
Also... If you are not buying that and think it's just nonsensical playing... I say the following...
It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
And if you think this is just child's play - read the paper: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdf

Check our sponsor The Great CoursesPlus (free trial): http://ow.ly/j5cB30hIvm2
This video features Cliff Stoll.
More links & stuff in full description below ↓↓↓
More Cliff Stoll videos: http://bit.ly/Cliff_Videos
Buy a Klein Bottle from Cliff - it's an experience: http://www.kleinbottle.com
Discuss this video on Brady's subreddit: https://redd.it/96x6c4
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Additional animation by Pete McPartlan
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Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
People and institutions featured in videos are not affiliated with episode sponsors.
The Great Courses Plus is currently available to watch through a web browser to almost anyone in the world and optimized for the US, UK, and Australian markets. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally.

Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help
More links & stuff in full description below ↓↓↓
EXTRAARTICLE BY TONY: http://bit.ly/TonyResponse
The sum of all natural numbers (from 1 to infinity) produces an "astounding" result.
ANOTHER PROOF & EXTRA FOOTAGE: http://youtu.be/E-d9mgo8FGk
MORE: http://youtu.be/0Oazb7IWzbA
NY Times article on this: http://nyti.ms/1iftqSv
TonyPadilla and Ed Copeland are physicists at the University of Nottingham.
They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols
Grandi's Series: 1-1+1-1.... http://www.youtube.com/watch?v=PCu_BNNI5x4
Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series
We also here that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it.
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady HaranBrady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile

published:09 Jan 2014

views:6692422

FeaturingHollyKrieger...Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
More links & stuff in full description below ↓↓↓
With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
Check out the monster dollar game shown in the video here: http://www.bradyharanblog.com/blog/the-dollar-game
More videos with Holly: http://bit.ly/HollyKrieger
Read more on this: https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
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Sign up for (occasional) emails: http://eepurl.com/YdjL9

published:31 Aug 2018

views:224840

With Dr HollyKrieger from Murray Edwards College, University of Cambridge.
Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile
More links & stuff in full description below ↓↓↓
More Numberphile videos with Dr Krieger: http://bit.ly/HollyKrieger
Her Twitter: https://twitter.com/hollykrieger
Some more reading on the topic: http://www.ams.org/journals/bull/2004-41-01/S0273-0979-03-00993-5/S0273-0979-03-00993-5.pdfOpenProblemsGroup on Brilliant: https://brilliant.org/groups/open-problems-group
Editing and animation by Pete McPartlan
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
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Subscribe: http://bit.ly/Numberphile_Sub
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(*) Among current mathematicians, many people regard Professor Tao as the world's finest... Opinions on such things vary, of course.
Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers.
EXTRA FOOTAGE: https://youtu.be/48Hr3CT5Tpk (and more extras to come)
The Legend of Question Six: https://youtu.be/Y30VF3cSIYQ
Professor Tao's blog: https://terrytao.wordpress.com/
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
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Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
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Sign up for (occasional) emails: http://eepurl.com/YdjL9

published:14 Mar 2017

views:1937095

The JosephusProblem, featuring Daniel Erman from University of Wisconsin-Madison.
Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k
More links & stuff in full description below ↓↓↓
Correction: Around 9:40 that should be L less than 2^a NOT 2a --- Sorry, typo in editing! But you got the point hopefully.
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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Number (magazine)

Number is the leading Japanesesportsmagazine published on every Thursday by Bungeishunju. The official name is Sports Graphic Number. Though the circulation once hit 47 million, it is now around 10 million.

The first issue, released in April 1980, drew attention by the piece Enatsu's 21 balls(江夏の21球,Enatsu no 21 kyu). Yet the magazine failed to return a profit for the next 10 years. Today however, the magazine is one of the most profitable publications of Bungeishunju. The success of the magazine also led other rival publishers to launch sports magazines, though they tend to be less successful.

References

Non-geographic telephone numbers in the United Kingdom

A non-geographic number is a type of telephone number that is not linked to any specific locality. Such numbers are an alternative to the traditional 'landline' numbers that are assigned geographically using a system of location-specific area codes.
Non-geographic numbers are used for various reasons, from providing flexible routeing of incoming phone calls to generating revenue for paid-for services.

Functionality

Non-geographic numbers were introduced to offer services that were historically unavailable on standard landline phone numbers, particularly in terms of call routeing and special charging arrangements.
Advertised benefits of non-geographic numbers include:

Call Routing. Calls can be flexibly redirected to virtually any destination. For example, calls could be answered in different call centres depending on where the caller is located or the time of day.

Ease of Communication. Organisations covering multiple locations can advertise a single national phone number rather than having to publicise different numbers for different areas.

Premium-rate telephone number

Premium-rate telephone numbers are telephone numbers for telephone calls during which certain services are provided, and for which prices higher than normal are charged. Unlike a normal call, part of the call charge is paid to the service provider, thus enabling businesses to be funded via the calls. While the billing is different, calls are usually routed the same way they are for a toll-free telephone number, being anywhere despite the area code used. These telephone numbers are usually allocated from a national telephone numbering plan in such a way that they are easily distinguished from other numbers. Telephone companies typically offer blocking services to allow telephone customers to prevent access to these number ranges from their telephones. In some jurisdictions, telephone companies are required by law to offer such blocking.

In 2007, Haran worked as a filmmaker-in-residence for Nottingham Science City, as part of an agreement between the BBC and The University of Nottingham. His "Test Tube" project started with the idea of producing a documentary about scientists and their research, but he decided to upload his raw footage to YouTube; from that point "Periodic Videos" and "Sixty Symbols" were developed. Haran then left the BBC to work full-time making YouTube videos.

Research institute

A research institute is an establishment endowed for doing research. Research institutes may specialize in basic research or may be oriented to applied research. Although the term often implies natural science research, there are also many research institutes in the social sciences as well, especially for sociological and historical research purposes.

History

MSRI was founded in 1982 by Shiing-Shen Chern, Calvin Moore, and Isadore M. Singer. MSRI hosts about 85 mathematicians and postdoctoral research fellows each semester for extended stays and holds programs and workshops, which draw approximately 2,000 visits by mathematical scientists throughout the year. Unlike many mathematical institutes, it has no permanent faculty or members, and its scientific activities are overseen by its Directorate and its Scientific Advisory Committee, a panel of distinguished mathematicians drawn from a variety of different areas of mathematical research.

The Most Evil Number - Numberphile

Is there a more evil number than Belphegor's Prime...Don't miss the extra footage on Numberphile2: https://youtu.be/9CcI5M1LfRs
More links & stuff in full description below ↓↓↓
This video features ProfessorTonyPadilla from the University of Nottingham.
More Tony videos: http://bit.ly/Padilla_Numberphile
666 video: https://youtu.be/UkZqFtYtqaI
BeastlyPrimes: https://oeis.org/A131645
Belphegor Primes: https://oeis.org/A232448
Republican Primes: https://oeis.org/A125524
Democratic Primes: https://oeis.org/A125523
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
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Sign up for (occasional) emails: http://eepurl.com/YdjL9

12:58

Primes on the Moon (Lunar Arithmetic) - Numberphile

Primes on the Moon (Lunar Arithmetic) - Numberphile

Primes on the Moon (Lunar Arithmetic) - Numberphile

FeaturingNeil Sloane from the Online Encyclopedia of Integer Sequences (OEIS). LunarArithmetic (aka Dismal Arithmetic)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of the OEIS: https://oeis.org
Lunar Primes: https://oeis.org/A087097
Lunar Squares: https://oeis.org/A087019
The original paper on lunar arithmetic (formerly dismal arithmetic) by David Applegate, Marc LeBrun, and Neil Sloane: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdfSloane's Gap: https://youtu.be/_YysNM2JoFo
Six Sequences: https://youtu.be/VDD6FDhKCYA
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Patreon: http://www.patreon.com/numberphile
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
----------------
As expected many people ask "what is the point of this"... And fair enough.
Rather than answering everyone individually, here is my view (I am just the film-maker, not a mathematician)
- Brady
↓↓↓
1. Because it is fun and creative - and playing with new ideas is good for your brain.
2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that.
Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope not!!!)... But neither is it just throwing ALL rules out of the window... It is creating a new arbitrary set of rules and seeing what happens...
What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics?
Also... If you are not buying that and think it's just nonsensical playing... I say the following...
It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
And if you think this is just child's play - read the paper: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdf

5-Sided Square - Numberphile

Check our sponsor The Great CoursesPlus (free trial): http://ow.ly/j5cB30hIvm2
This video features Cliff Stoll.
More links & stuff in full description below ↓↓↓
More Cliff Stoll videos: http://bit.ly/Cliff_Videos
Buy a Klein Bottle from Cliff - it's an experience: http://www.kleinbottle.com
Discuss this video on Brady's subreddit: https://redd.it/96x6c4
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
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Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Additional animation by Pete McPartlan
Patreon: http://www.patreon.com/numberphile
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
People and institutions featured in videos are not affiliated with episode sponsors.
The Great Courses Plus is currently available to watch through a web browser to almost anyone in the world and optimized for the US, UK, and Australian markets. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally.

ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help
More links & stuff in full description below ↓↓↓
EXTRAARTICLE BY TONY: http://bit.ly/TonyResponse
The sum of all natural numbers (from 1 to infinity) produces an "astounding" result.
ANOTHER PROOF & EXTRA FOOTAGE: http://youtu.be/E-d9mgo8FGk
MORE: http://youtu.be/0Oazb7IWzbA
NY Times article on this: http://nyti.ms/1iftqSv
TonyPadilla and Ed Copeland are physicists at the University of Nottingham.
They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols
Grandi's Series: 1-1+1-1.... http://www.youtube.com/watch?v=PCu_BNNI5x4
Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series
We also here that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it.
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady HaranBrady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
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Other merchandise: https://store.dftba.com/collections/numberphile

11:58

The Dollar Game - Numberphile

The Dollar Game - Numberphile

The Dollar Game - Numberphile

FeaturingHollyKrieger...Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
More links & stuff in full description below ↓↓↓
With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
Check out the monster dollar game shown in the video here: http://www.bradyharanblog.com/blog/the-dollar-game
More videos with Holly: http://bit.ly/HollyKrieger
Read more on this: https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
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Subscribe: http://bit.ly/Numberphile_Sub
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Sign up for (occasional) emails: http://eepurl.com/YdjL9

8:06

Catalan's Conjecture - Numberphile

Catalan's Conjecture - Numberphile

Catalan's Conjecture - Numberphile

With Dr HollyKrieger from Murray Edwards College, University of Cambridge.
Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile
More links & stuff in full description below ↓↓↓
More Numberphile videos with Dr Krieger: http://bit.ly/HollyKrieger
Her Twitter: https://twitter.com/hollykrieger
Some more reading on the topic: http://www.ams.org/journals/bull/2004-41-01/S0273-0979-03-00993-5/S0273-0979-03-00993-5.pdfOpenProblemsGroup on Brilliant: https://brilliant.org/groups/open-problems-group
Editing and animation by Pete McPartlan
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
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The World's Best Mathematician (*) - Numberphile

(*) Among current mathematicians, many people regard Professor Tao as the world's finest... Opinions on such things vary, of course.
Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers.
EXTRA FOOTAGE: https://youtu.be/48Hr3CT5Tpk (and more extras to come)
The Legend of Question Six: https://youtu.be/Y30VF3cSIYQ
Professor Tao's blog: https://terrytao.wordpress.com/
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
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13:58

The Josephus Problem - Numberphile

The Josephus Problem - Numberphile

The Josephus Problem - Numberphile

The JosephusProblem, featuring Daniel Erman from University of Wisconsin-Madison.
Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k
More links & stuff in full description below ↓↓↓
Correction: Around 9:40 that should be L less than 2^a NOT 2a --- Sorry, typo in editing! But you got the point hopefully.
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9:16

Graham's Number - Numberphile

Graham's Number - Numberphile

Graham's Number - Numberphile

A number so epic it will collapse your brain into a black hole! Yet TonyPadilla and Matt Parker take the risk of discussing its magnitude. Watch with caution.
More links & stuff in full description below ↓↓↓
See also our video about the Googol and Googolplex at: http://www.youtube.com/watch?v=8GEebx72-qs
More about Matt and Tony at: http://www.numberphile.com/team/index.html
Matt's section filmed at the Champagne Bar at St Pancras train station.
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7:36

Zero Factorial - Numberphile

Zero Factorial - Numberphile

Zero Factorial - Numberphile

0! = 1
Dr JamesGrime tries to explain why this is the case - follow James on Twitter at https://twitter.com/jamesgrime
More links & stuff in full description below ↓↓↓
Regarding the equation at the end - James says it should be e^-t dt NOT e^-n dn ... sorry for the mix-up!
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9:03

Weber's Law - Numberphile

Weber's Law - Numberphile

Weber's Law - Numberphile

Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile (sponsor)
Hannah Fry has a new book coming: https://amzn.to/2J6oCph (US) or https://amzn.to/2KVfXDD (UK)
More links & stuff in full description below ↓↓↓
A little extra bit from this interview: https://youtu.be/R1YWefm-o6c
This video features Hannah Fry. Her new book "Hello World" is out soon.
Hannamation in this video by Pete McPartlan.
More Hannah on Numberphile: http://bit.ly/hannah_vids
Some extra out-take video from Hannah's stint behind the camera is available to Patrons!!!
https://www.patreon.com/posts/19022716
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
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The World's Best Mathematician (*) - Numberphile

(*) Among current mathematicians, many people regard Professor Tao as the world's finest... Opinions on such things vary, of course.
Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers.
EXTRA FOOTAGE: https://youtu.be/48Hr3CT5Tpk (and more extras to come)
The Legend of Question Six: https://youtu.be/Y30VF3cSIYQ
Professor Tao's blog: https://terrytao.wordpress.com/
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
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Numberphile tweets: https:...

Graham's Number - Numberphile

A number so epic it will collapse your brain into a black hole! Yet TonyPadilla and Matt Parker take the risk of discussing its magnitude. Watch with caution.
More links & stuff in full description below ↓↓↓
See also our video about the Googol and Googolplex at: http://www.youtube.com/watch?v=8GEebx72-qs
More about Matt and Tony at: http://www.numberphile.com/team/index.html
Matt's section filmed at the Champagne Bar at St Pancras train station.
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Brady's l...

published: 04 Apr 2012

Zero Factorial - Numberphile

0! = 1
Dr JamesGrime tries to explain why this is the case - follow James on Twitter at https://twitter.com/jamesgrime
More links & stuff in full description below ↓↓↓
Regarding the equation at the end - James says it should be e^-t dt NOT e^-n dn ... sorry for the mix-up!
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published: 08 Jun 2013

Weber's Law - Numberphile

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Hannah Fry has a new book coming: https://amzn.to/2J6oCph (US) or https://amzn.to/2KVfXDD (UK)
More links & stuff in full description below ↓↓↓
A little extra bit from this interview: https://youtu.be/R1YWefm-o6c
This video features Hannah Fry. Her new book "Hello World" is out soon.
Hannamation in this video by Pete McPartlan.
More Hannah on Numberphile: http://bit.ly/hannah_vids
Some extra out-take video from Hannah's stint behind the camera is available to Patrons!!!
https://www.patreon.com/posts/19022716
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative de...

FeaturingNeil Sloane from the Online Encyclopedia of Integer Sequences (OEIS). LunarArithmetic (aka Dismal Arithmetic)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of the OEIS: https://oeis.org
Lunar Primes: https://oeis.org/A087097
Lunar Squares: https://oeis.org/A087019
The original paper on lunar arithmetic (formerly dismal arithmetic) by David Applegate, Marc LeBrun, and Neil Sloane: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdfSloane's Gap: https://youtu.be/_YysNM2JoFo
Six Sequences: https://youtu.be/VDD6FDhKCYA
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----------------
As expected many people ask "what is the point of this"... And fair enough.
Rather than answering everyone individually, here is my view (I am just the film-maker, not a mathematician)
- Brady
↓↓↓
1. Because it is fun and creative - and playing with new ideas is good for your brain.
2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that.
Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope not!!!)... But neither is it just throwing ALL rules out of the window... It is creating a new arbitrary set of rules and seeing what happens...
What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics?
Also... If you are not buying that and think it's just nonsensical playing... I say the following...
It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
And if you think this is just child's play - read the paper: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdf

FeaturingNeil Sloane from the Online Encyclopedia of Integer Sequences (OEIS). LunarArithmetic (aka Dismal Arithmetic)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of the OEIS: https://oeis.org
Lunar Primes: https://oeis.org/A087097
Lunar Squares: https://oeis.org/A087019
The original paper on lunar arithmetic (formerly dismal arithmetic) by David Applegate, Marc LeBrun, and Neil Sloane: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdfSloane's Gap: https://youtu.be/_YysNM2JoFo
Six Sequences: https://youtu.be/VDD6FDhKCYA
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
NUMBERPHILE
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Sign up for (occasional) emails: http://eepurl.com/YdjL9
----------------
As expected many people ask "what is the point of this"... And fair enough.
Rather than answering everyone individually, here is my view (I am just the film-maker, not a mathematician)
- Brady
↓↓↓
1. Because it is fun and creative - and playing with new ideas is good for your brain.
2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that.
Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope not!!!)... But neither is it just throwing ALL rules out of the window... It is creating a new arbitrary set of rules and seeing what happens...
What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics?
Also... If you are not buying that and think it's just nonsensical playing... I say the following...
It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
And if you think this is just child's play - read the paper: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdf

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This video features Cliff Stoll.
More links & stuff in full description below ↓↓↓
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Check our sponsor The Great CoursesPlus (free trial): http://ow.ly/j5cB30hIvm2
This video features Cliff Stoll.
More links & stuff in full description below ↓↓↓
More Cliff Stoll videos: http://bit.ly/Cliff_Videos
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Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
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And support from MathFor America - https://www.mathforamerica.org/
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People and institutions featured in videos are not affiliated with episode sponsors.
The Great Courses Plus is currently available to watch through a web browser to almost anyone in the world and optimized for the US, UK, and Australian markets. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally.

ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help
More links & stuff in full description below ↓↓↓
EXTRAARTICLE BY TONY...

Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help
More links & stuff in full description below ↓↓↓
EXTRAARTICLE BY TONY: http://bit.ly/TonyResponse
The sum of all natural numbers (from 1 to infinity) produces an "astounding" result.
ANOTHER PROOF & EXTRA FOOTAGE: http://youtu.be/E-d9mgo8FGk
MORE: http://youtu.be/0Oazb7IWzbA
NY Times article on this: http://nyti.ms/1iftqSv
TonyPadilla and Ed Copeland are physicists at the University of Nottingham.
They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols
Grandi's Series: 1-1+1-1.... http://www.youtube.com/watch?v=PCu_BNNI5x4
Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series
We also here that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it.
Support us on Patreon: http://www.patreon.com/numberphile
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Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help
More links & stuff in full description below ↓↓↓
EXTRAARTICLE BY TONY: http://bit.ly/TonyResponse
The sum of all natural numbers (from 1 to infinity) produces an "astounding" result.
ANOTHER PROOF & EXTRA FOOTAGE: http://youtu.be/E-d9mgo8FGk
MORE: http://youtu.be/0Oazb7IWzbA
NY Times article on this: http://nyti.ms/1iftqSv
TonyPadilla and Ed Copeland are physicists at the University of Nottingham.
They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols
Grandi's Series: 1-1+1-1.... http://www.youtube.com/watch?v=PCu_BNNI5x4
Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series
We also here that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it.
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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FeaturingHollyKrieger...Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
More links & stuff in full description below ↓↓↓
With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
Check out the monster dollar game shown in the video here: http://www.bradyharanblog.com/blog/the-dollar-game
More videos with Holly: http://bit.ly/HollyKrieger
Read more on this: https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
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FeaturingHollyKrieger...Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
More links & stuff in full description below ↓↓↓
With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
Check out the monster dollar game shown in the video here: http://www.bradyharanblog.com/blog/the-dollar-game
More videos with Holly: http://bit.ly/HollyKrieger
Read more on this: https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from MathFor America - https://www.mathforamerica.org/
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With Dr HollyKrieger from Murray Edwards College, University of Cambridge.
Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile
More links & stuff in full description below ↓↓↓
More Numberphile videos with Dr Krieger: http://bit.ly/HollyKrieger
Her Twitter: https://twitter.com/hollykrieger
Some more reading on the topic: http://www.ams.org/journals/bull/2004-41-01/S0273-0979-03-00993-5/S0273-0979-03-00993-5.pdfOpenProblemsGroup on Brilliant: https://brilliant.org/groups/open-problems-group
Editing and animation by Pete McPartlan
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by ScienceSandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
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With Dr HollyKrieger from Murray Edwards College, University of Cambridge.
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More links & stuff in full description below ↓↓↓
More Numberphile videos with Dr Krieger: http://bit.ly/HollyKrieger
Her Twitter: https://twitter.com/hollykrieger
Some more reading on the topic: http://www.ams.org/journals/bull/2004-41-01/S0273-0979-03-00993-5/S0273-0979-03-00993-5.pdfOpenProblemsGroup on Brilliant: https://brilliant.org/groups/open-problems-group
Editing and animation by Pete McPartlan
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NUMBERPHILE
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The JosephusProblem, featuring Daniel Erman from University of Wisconsin-Madison.
Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k
More links & stuff in full description below ↓↓↓
Correction: Around 9:40 that should be L less than 2^a NOT 2a --- Sorry, typo in editing! But you got the point hopefully.
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NUMBERPHILE
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The JosephusProblem, featuring Daniel Erman from University of Wisconsin-Madison.
Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k
More links & stuff in full description below ↓↓↓
Correction: Around 9:40 that should be L less than 2^a NOT 2a --- Sorry, typo in editing! But you got the point hopefully.
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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Weber's Law - Numberphile

Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile (sponsor)
Hannah Fry has a new book coming: https://amzn.to/2J6oCph (US) or ...

Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile (sponsor)
Hannah Fry has a new book coming: https://amzn.to/2J6oCph (US) or https://amzn.to/2KVfXDD (UK)
More links & stuff in full description below ↓↓↓
A little extra bit from this interview: https://youtu.be/R1YWefm-o6c
This video features Hannah Fry. Her new book "Hello World" is out soon.
Hannamation in this video by Pete McPartlan.
More Hannah on Numberphile: http://bit.ly/hannah_vids
Some extra out-take video from Hannah's stint behind the camera is available to Patrons!!!
https://www.patreon.com/posts/19022716
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
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Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile (sponsor)
Hannah Fry has a new book coming: https://amzn.to/2J6oCph (US) or https://amzn.to/2KVfXDD (UK)
More links & stuff in full description below ↓↓↓
A little extra bit from this interview: https://youtu.be/R1YWefm-o6c
This video features Hannah Fry. Her new book "Hello World" is out soon.
Hannamation in this video by Pete McPartlan.
More Hannah on Numberphile: http://bit.ly/hannah_vids
Some extra out-take video from Hannah's stint behind the camera is available to Patrons!!!
https://www.patreon.com/posts/19022716
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
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Primes on the Moon (Lunar Arithmetic) - Numberphile

FeaturingNeil Sloane from the Online Encyclopedia of Integer Sequences (OEIS). LunarArithmetic (aka Dismal Arithmetic)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of the OEIS: https://oeis.org
Lunar Primes: https://oeis.org/A087097
Lunar Squares: https://oeis.org/A087019
The original paper on lunar arithmetic (formerly dismal arithmetic) by David Applegate, Marc LeBrun, and Neil Sloane: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdfSloane's Gap: https://youtu.be/_YysNM2JoFo
Six Sequences: https://youtu.be/VDD6FDhKCYA
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----------------
As expected many people ask "what is the point of this"... And fair enough.
Rather than answering everyone individually, here is my view (I am just the film-maker, not a mathematician)
- Brady
↓↓↓
1. Because it is fun and creative - and playing with new ideas is good for your brain.
2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that.
Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope not!!!)... But neither is it just throwing ALL rules out of the window... It is creating a new arbitrary set of rules and seeing what happens...
What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics?
Also... If you are not buying that and think it's just nonsensical playing... I say the following...
It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
And if you think this is just child's play - read the paper: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdf

5-Sided Square - Numberphile

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This video features Cliff Stoll.
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ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help
More links & stuff in full description below ↓↓↓
EXTRAARTICLE BY TONY: http://bit.ly/TonyResponse
The sum of all natural numbers (from 1 to infinity) produces an "astounding" result.
ANOTHER PROOF & EXTRA FOOTAGE: http://youtu.be/E-d9mgo8FGk
MORE: http://youtu.be/0Oazb7IWzbA
NY Times article on this: http://nyti.ms/1iftqSv
TonyPadilla and Ed Copeland are physicists at the University of Nottingham.
They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols
Grandi's Series: 1-1+1-1.... http://www.youtube.com/watch?v=PCu_BNNI5x4
Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series
We also here that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it.
Support us on Patreon: http://www.patreon.com/numberphile
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The Dollar Game - Numberphile

FeaturingHollyKrieger...Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
More links & stuff in full description below ↓↓↓
With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
Check out the monster dollar game shown in the video here: http://www.bradyharanblog.com/blog/the-dollar-game
More videos with Holly: http://bit.ly/HollyKrieger
Read more on this: https://mattbaker.blog/2013/10/18/riemann-roch-for-graphs-and-applications/
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Catalan's Conjecture - Numberphile

With Dr HollyKrieger from Murray Edwards College, University of Cambridge.
Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile
More links & stuff in full description below ↓↓↓
More Numberphile videos with Dr Krieger: http://bit.ly/HollyKrieger
Her Twitter: https://twitter.com/hollykrieger
Some more reading on the topic: http://www.ams.org/journals/bull/2004-41-01/S0273-0979-03-00993-5/S0273-0979-03-00993-5.pdfOpenProblemsGroup on Brilliant: https://brilliant.org/groups/open-problems-group
Editing and animation by Pete McPartlan
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
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The Josephus Problem - Numberphile

The JosephusProblem, featuring Daniel Erman from University of Wisconsin-Madison.
Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k
More links & stuff in full description below ↓↓↓
Correction: Around 9:40 that should be L less than 2^a NOT 2a --- Sorry, typo in editing! But you got the point hopefully.
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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Number (magazine)

Number is the leading Japanesesportsmagazine published on every Thursday by Bungeishunju. The official name is Sports Graphic Number. Though the circulation once hit 47 million, it is now around 10 million.

The first issue, released in April 1980, drew attention by the piece Enatsu's 21 balls(江夏の21球,Enatsu no 21 kyu). Yet the magazine failed to return a profit for the next 10 years. Today however, the magazine is one of the most profitable publications of Bungeishunju. The success of the magazine also led other rival publishers to launch sports magazines, though they tend to be less successful.